A cylindrical tank with axis horizontal has a diameter d and a length L. It holds oil to depth d ( d<D ) when a leak starts to drain off the oil at a constant rate k. How fast is the level falling

Answer 1

https://en.wikipedia.org/wiki/Circular_segment

So you want the area not shaded, PI*r^2-areasegment.
I suspect you will have to work this in two cases:
a) D/2 <d<D and b) 0<d<D/2, and the levels rates will be falling at diffent rates depending on which case.